Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
int main(){
    int N;
    cin>>N;
    int a[1000];
    for (int i=0; i<N; i++)cin>>a[i];
    
    sort(a, a+N, greater<int>());
    double ans=0;
    for (int i=0; i<N-1; i++) {
        if(i==0)ans=max(ans,(double)(a[2]+a[3])/(a[0]-a[1]));
        else if(i==1)ans=max(ans,(double)(a[2]+a[3])/(a[1]-a[2]));
        else ans=max(ans,(double)(a[0]+a[1])/(a[i]-a[i+1]));
    }
    printf("%0.5f\n",ans);
    return 0;
}